(i) Field of the Invention
This invention relates to a transversal filter and to an echo canceller employing such a filter.
Transversal filters employing tapped delay lines to generate delayed versions of a signal applied to the filter are well known. The delayed signal versions are multiplied by predetermined multiplication coefficients and accumulated to produce a filtered output signal having characteristics determined by the predetermined coefficients. Such arrangements have particular application in echo cancellers for communications links where echo signals present in a four wire communications link can be cancelled by connecting the filter across input and output connections of the four wire link to hybrids providing junctions between the four wire link and respective two wire links. Means is provided for adjusting the multiplying coefficients as necessary to effect echo cancelling. Cancellers of this kind have the advantage that they can be arranged to provide for time-variation of the multiplication coefficients so that the characteristics of the filter can be adjusted to effect echo cancellation even where the characteristics of the four wire link are changing at appreciable rates.
(ii) Prior Art
Transversal filters and echo cancellers of the above kind have been the subject of considerable development work and have been described in numerous prior publications. Particularly, Australian Patent specification No. 435,932 (Western Electric Company) describes the basic form of the transversal structure for an adaptive echo canceller. The article "Echo Cancellation on Time Variant Circuits" by N. Demytko and K. S. English published in the proceedings of the IEEE, Vol. 65, No. 3, March 1977 at pages 444-453 contains a general description of such cancellers and the incorporated transversal filters.
One form of transversal filter can be constructed where the delay line comprises electric signal delay elements which provide an output signal varying continuously in time. As is well known, the impulse response of such a delay element is represented by the expression: EQU .delta.(.tau.-T)
where
.delta.(.tau.) is the Dirac delta function, PA1 T is the transmission delay introduced by the element. PA1 N is the number of stored coefficients, PA1 T is the time spacing of samples of the input signal PA1 .tau. is the time interval and PA1 f(.tau.) is the impulse response of a filter accounting for extraneous linear filtering, independent of the coefficients h.sub.i The convolution operator "*" is defined such that a relationship of the form h(.tau.)*g(.tau.) represents the integral relationship ##EQU6## PA1 N is the number of stored coefficients, PA1 f(.tau.) is an impulse response accounting for fixed linear filtering at the input and output, independent of the settings h.sub.i, and PA1 .delta.(.tau.-.tau..sub.i) is the Dirac delta function defined as a function of time interval .tau. and of a set of time delays .tau..sub.i, where .tau..sub.i is not equal to iT. Preferably, the set of time delays .tau..sub.i are defined as follows: ##EQU8## The invention also provides a filter having an overall impulse response of the form ##EQU9## and producing, from an applied input x(t) an output ##EQU10## where y(t) is obtained by lowpass filtering of a waveform x(t) in use generated in the filter, where z(t) takes the form: ##EQU11## PA1 (a) sampling means for sampling the input signal at consecutive equi time-spaced intervals T to produce the sequence of consecutive samples x.sub.n (n= . . . ,0,1,2,3, . . . ); PA1 (b) first storing means for storing consecutive sets of said samples, each such set, S.sub.i (i=-.infin., . . . 0, . . . .infin.) comprising the N samples x.sub.i-k (k=0,1, . . . N-1); PA1 (c) second storing means for storing N coefficients h.sub.k (k=0,1, . . . , N-1) together representing a linear filter impulse response; PA1 (d) generating means for generating from each said set of stored samples, and from the impulse response coefficients stored in said second storing means, the products h.sub.k .multidot.x.sub.i-k' and for presenting these as product signals at an output from the generating means; and PA1 (e) a lowpass filter connected to receive the said product signals and to generate the said output signal by lowpass filtering the product signals
By cascading N such delay elements and summing the outputs from each delay element with weighting coefficients h.sub.i, an impulse response can be realised which is represented by the expression: ##EQU4## Such a filter is described in the aforementioned Australian patent specification No. 435,932.
Another form of transversal filter employs a sampling technique in which samples of the input signal are taken at equi-spaced time intervals T, and stored in digital form. If the input signal is known to contain no frequency components above 1/2T, it then follows from the Shannon sampling theorem that the unsampled input signal can be reconstructed at all times instants from the stored samples. After each acquisition of a new input sample, the stored samples are multiplied by the respective stored coefficients to produce a series of product signals. These are summed then converted from digital to analogue representations and filtered with a lowpass filter of cut-off frequency 1/2T to produce the output signal. This technique is useful since the sample store can comprise a shift register which, after updating by acquisition of each new sample, is rapidly circulated together with the store for multiplier coefficients to effect time-sharing of a single high-speed multiplier over all multiplications operations. This circulation technique is described in greater detail in the book "Theory and Applications of Digital Signal Processing", by L. R. Rabiner and B. Gold, Prentice-Hill, 1975, pages 542-551.
Several alternate forms of such a filter are obtained by interchanging the order of digital to analogue conversion and the multiplication and summation operations.
All such realisations of transversal filters are characterised by an overall impulse response defined by the convolution relationship: ##EQU5## In the above: h.sub.i represent the multiplier coefficients,
The present invention is based on the realisation that the impulse response of the overall filter can, with advantage, be modified from the above to provide a physical structure which can be simpler in form.